Unable to select items on outliner
In the Outliner, when you click on the object mesh icon, it allows you to enter in Edit mode and to edit the object mesh, it doesn't allow you to precisely select one part of the mesh if that's what you're trying. If you don't see anything when you click on this icon, maybe it's because your object is not visible on your 3D View, it can be on another layer for example. Also, when you try to edit an object, why don't you select it and press tab to enter in Edit mode? This is the classic method.

About your display problem: You must accidentally press Z, it makes you switch between Rendered (or Material) mode and Wireframe view. See what happens on the bottom horizontal bar of your 3D View.